Asymptotic stability of linear stochastic differential equations of neutral type

1992 ◽  
Vol 52 (2) ◽  
pp. 856-858
Author(s):  
L. E. Shaikhet
Keyword(s):  
Asymptotic Stability ◽  
Differential Equations ◽  
Stochastic Differential Equations ◽  
Neutral Type

scholarly journals Conditions to Guarantee the Existence of the Solution to Stochastic Differential Equations of Neutral Type

Symmetry ◽  
2020 ◽  
Vol 12 (10) ◽  
pp. 1613
Author(s):  
Mun-Jin Bae ◽  
Chan-Ho Park ◽  
Young-Ho Kim
Keyword(s):  
Differential Equations ◽  
Stochastic Differential Equations ◽  
Existence And Uniqueness ◽  
Neutral Type ◽  
Sufficient Conditions ◽  
Exponential Estimates ◽  
Analysis Theory ◽  
Linear Growth Condition ◽  
Uniqueness Of The Solution ◽  
The Uniqueness Theorem

The main purpose of this study was to demonstrate the existence and the uniqueness theorem of the solution of the neutral stochastic differential equations under sufficient conditions. As an alternative to the stochastic analysis theory of the neutral stochastic differential equations, we impose a weakened Ho¨lder condition and a weakened linear growth condition. Stochastic results are obtained for the theory of the existence and uniqueness of the solution. We first show that the conditions guarantee the existence and uniqueness; then, we show some exponential estimates for the solutions.

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